This paper proposes the first known to us iris recognition methodology designed specifically for post-mortem samples. We propose to use deep learning-based iris segmentation models to extract highly irregular iris texture areas in post-mortem iris images. We show how to use segmentation masks predicted by neural networks in conventional, Gabor-based iris recognition method, which employs circular approximations of the pupillary and limbic iris boundaries. As a whole, this method allows for a significant improvement in post-mortem iris recognition accuracy over the methods designed only for ante-mortem irises, including the academic OSIRIS and commercial IriCore implementations. The proposed method reaches the EER less than 1% for samples collected up to 10 hours after death, when compared to 16.89% and 5.37% of EER observed for OSIRIS and IriCore, respectively. For samples collected up to 369 hours post-mortem, the proposed method achieves the EER 21.45%, while 33.59% and 25.38% are observed for OSIRIS and IriCore, respectively. Additionally, the method is tested on a database of iris images collected from ophthalmology clinic patients, for which it also offers an advantage over the two remaining methods. This work is the first step towards post-mortem-specific iris recognition, which increases the chances of identification of deceased subjects in forensic investigations. The new database of post-mortem iris images acquired from 42 subjects, as well as the deep learning-based segmentation models are made available along with the paper, to ensure all the results presented in this manuscript are reproducible.